Nuclear & Particle Physics - Compton Scattering

In the Compton effect, a photon with energy E scatters through 90^o angle from stationary electron mass m. The energy of the scattered photon is

A. E
B. E/2
C. E²/mc²
D. E²/(E + mc²)
E. E∙mc²/(E + mc²)

(GR0877 #97)

Solution: 

Compton scattering: λ_f − λ_i = ^h/_mc (1− cosθ)
Photon energy, E = ^hc/_λ

^hc/_Ef − ^hc/_E = ^h/_mc (1 − cos 90^o)
¹/_Ef − ¹/_E = ¹/_mc² (1 − 0)
¹/_Ef  = ¹/_mc² + ¹/_E
^Emc2/_Ef  = E + mc^2
Emc2/_Ef  = E + mc²
E_f  = ^Emc2/_{E + mc²} 

Answer: E